Improving Antibody-Antigen Interaction Prediction Through Flexibility

with ESMFold

Sara Joubbi

1,2 a

, Giuseppe Maccari

2 b

, Giorgio Ciano

2 c

, Alessio Micheli

1 d

Paolo Milazzo

1 e

and Duccio Medini

2 f

Department of Computer Science, University of Pisa, Pisa, Italy

Data Science for Health Lab, Fondazione Toscana Life Sciences, Siena, Italy

Keywords:

Antibody, Antigen, Fingerprint, Deep Learning, Flexibility, ESMFold.

Abstract:

Antibodies are essential proteins in the immune system due to their capacity to bind to speciﬁc antigens.

They also play a critical role in developing vaccines and treatments for infectious diseases. Their complex

structure, with variable regions for antigen binding and ﬂexible hinge regions, presents challenges for ac-

curate computational modeling. Recent advancements in deep learning have revolutionized protein structure

prediction. Despite these advancements, predicting interactions between antibodies and antigens remains chal-

lenging, mainly due to the ﬂexibility of antibodies and the dynamic nature of binding events. This study uses

ﬁngerprint-based methodologies that incorporate ESMFold conﬁdence scores as a ﬂexibility feature to model

Ab-Ag interactions. Our methodology shows how including ﬂexibility has improved Ab-Ag interactions by

3%, achieving an AUC-ROC of 91%.

1 INTRODUCTION

Antibodies are essential immune system proteins, re-

sponsible for identifying and binding to speciﬁc anti-

gens, such as pathogens or foreign substances, to neu-

tralize or mark them for destruction by other immune

cells (Kindt et al., 2007). This highly selective bind-

ing ability plays a critical role in immune defense and

makes antibodies invaluable tools in biotherapeutics.

They are widely used in developing treatments for

various diseases, including cancers, autoimmune dis-

orders, and infectious diseases, where they can target

speciﬁc molecules or cells with precision, minimizing

damage to healthy tissues (Kaplon et al., 2023).

Structurally, antibodies are Y-shaped proteins

composed of two heavy (H) and light (L) chains. Each

pair forms a variable (V) region that binds antigens,

while the constant (C) region, held together by disul-

ﬁde bonds, binds to receptors and maintains protein

integrity (Joubbi et al., 2024) (see Figure 1A). Anti-

https://orcid.org/0009-0002-1079-7204

https://orcid.org/0000-0002-2894-3583

https://orcid.org/0000-0003-2863-4315

https://orcid.org/0000-0001-5764-5238

https://orcid.org/0000-0002-7309-6424

https://orcid.org/0000-0001-6041-2603

bodies present ﬂexible hinge regions that connect the

antigen-binding fragment (Fab) to the crystallizable

fragment (Fc), enabling dynamic movement between

these regions. This ﬂexibility allows the antibody

to better interact with various antigens and immune

receptors. Additionally, post-translational modiﬁca-

tions, like glycosylation, play a critical role in reg-

ulating the antibody’s structure and function. Gly-

cosylation can inﬂuence the antibody’s stability, im-

mune recognition, and effector functions, contribut-

ing to its overall complexity and adaptability in im-

mune responses (Guo et al., 2024).

The ﬁeld of antibody-based treatments is grow-

ing rapidly, as shown by the increasing number of

FDA approvals, clinical trials, and patent applications

(Wilman et al., 2022). The market for antibody thera-

pies is projected to surpass $400 billion by 2028, with

an annual growth rate of 14.1% (Larrosa et al., 2023;

Joubbi et al., 2024). Traditionally, antibody devel-

opment depends on labor-intensive and costly tech-

niques such as phage display and animal immuniza-

tion. However, the incorporation of computational

tools in pharmaceutical research is expected to greatly

reduce the costs and time associated with developing

new antibodies. This progress is expected to make

immunotherapy more affordable and suitable for a

broader range of diseases.

Joubbi, S., Maccari, G., Ciano, G., Micheli, A., Milazzo, P. and Medini, D.

Improving Antibody-Antigen Interaction Prediction Through Flexibility with ESMFold.

DOI: 10.5220/0013189500003911

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 18th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2025) - Volume 1, pages 603-610

ISBN: 978-989-758-731-3; ISSN: 2184-4305

603

Figure 1: Antibody structure and ﬂexibility. A) The heavy

chain (H) of the antibody is shown in blue, while the light

chain (L) is depicted in orange. On the right, a focus on

a CDR is shown with labeled light and heavy chain CDR

loops (PDB 3IY3). The Fab region is formed by the variable

regions and part of the constant (C) regions. The variable

regions (VH and VL) form the Fv region. The Fc region

contains the constant part of the chain. The antibody is a

ﬂexible molecule due to the Fab rotation and Hinge ﬂexibil-

ity. B) An example of antibody ﬂexibility after binding to

an antigen. Additionally, there is a change in conformation

at the binding site with the antigen. The antibody can then

form different Fc-Fc conﬁgurations with another antibody

or bind with a cell receptor.

Deep Learning (DL) methods have addressed var-

ious biological challenges, notably with AlphaFold2

(AF2) (Jumper et al., 2021), which have transformed

structural biology by accurately predicting protein 3D

structures from amino acid sequences. AF2, despite

its success, relies on multiple sequence alignments

(MSAs), which are less effective for antibody fold-

ing due to the high variability and lack of evolution-

ary data in CDR H3 loop sequences (Joubbi et al.,

2024). Alternative methods have been developed to

overcome this limitation. ESMFold uses ESM-2 for

comprehensive embedded representations of protein

sequences, providing a viable alternative to MSAs

(Lin et al., 2023). ESMFold outperforms AF2 when

utilizing only the amino acid sequence, achieving a

TM-Score of 0.68 compared to AF2’s 0.37, while also

providing faster predictions (Bertoline et al., 2023).

Accurate prediction of paratope and epitope re-

gions is crucial for antibody design. While antibody-

antigen (Ab-Ag) interactions are a type of protein-

protein interaction (PPI), they have distinct char-

acteristics that make general PPI prediction meth-

ods less effective for antibody applications (Graves

et al., 2020). Several DL methods have been de-

veloped to address PPIs, including ﬁngerprint (sur-

face) methods such as MaSIF (Gainza et al., 2020)

and dMaSIF (Sverrisson et al., 2021), as well as

PeSTo (Krapp et al., 2023). Additionally, speciﬁc

methods have been created for antibodies, such as

EMPM (Del Vecchio et al., 2021), PECAN (Pit-

tala and Bailey-Kellogg, 2020), and ﬁngerprint-based

techniques like Surface ID (Riahi et al., 2023).

Future directions for modeling antibody-antigen

(Ab-Ag) interactions involve representing antibody

ﬂexibility (Guo et al., 2024; Rudden et al., 2022;

Joubbi et al., 2024), as the paratope is characterized

by a certain level of ﬂexibility (Wang et al., 2013;

Rosen et al., 2005) as shown in Figure 1B. More-

over, the two protein structures slightly change during

binding (Pegoraro et al., 2023). While DL networks

can incorporate local ﬂexibility, they often struggle

with conformational switching (Rudden et al., 2022).

Addressing this remains a challenge, as long molecu-

lar dynamics simulations are computationally inten-

sive, and simpler analytical models, though faster,

may lack detail. Combining local contact models with

predicted Local Distance Difference Test (pLDDT)

scores can predict protein ﬂexibility faster (Ma et al.,

2023; Alderson et al., 2023; Alderson et al., 2023;

Middendorf and Eicholt, 2024). Building on this

approach, we use ESMFold’s pLDDT as a ﬂexibil-

ity feature for Ab-Ag interactions using ﬁngerprint

methodologies.

Main Contributions:

1. Application of the dMaSIF model to antibody-

antigen (Ab-Ag) interactions, incorporating pro-

tein ﬂexibility into the analysis.

2. Utilization of pLDDT scores to estimate the ﬂex-

ibility of Ab-Ag interactions, demonstrating the

potential for performance enhancement.

2 RELATED WORKS

Fischer in 1894 discovered that the interactions be-

tween molecules are heavily inﬂuenced by their struc-

ture and arrangement and successful binding relies

on the compatibility of geometric shapes (Fischer,

1894). Following this concept, several DL meth-

ods that target PPI and Ab-Ag interaction are based

on the structure and surface of the protein. PeSTo

(Krapp et al., 2023) is a revolutionary parameter-free

geometric transformer that directly manipulates the

atomic components of a protein structure. This in-

novative approach accurately predicts speciﬁc regions

on a protein surface that have the potential to in-

teract with other proteins, as well as nucleic acids,

lipids, ions, and small molecules. MaSIF (Gainza

et al., 2020) is another pioneering method that em-

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604

ploys DL and the concept of ﬁngerprints to forecast

PPIs. It accomplishes this by creating protein ﬁnger-

prints based on amino acid sequences, structural el-

ements, and functional motifs. The method divides

protein surfaces into patches and utilizes a convolu-

tional neural network (CNN) to identify interaction

sites and patterns. MaSIF has diverse applications, in-

cluding ligand binding (MaSIF-ligand), interface site

prediction (MaSIF-site), and partner binding predic-

tion (MaSIF-search). However, MaSIF’s reliance on

pre-computed features and meshes leads to slow per-

formance and high memory usage. To tackle these

issues, dMaSIF (Sverrisson et al., 2021) operates di-

rectly on raw 3D coordinates and atom types. It gen-

erates molecular surfaces on the ﬂy using a novel ge-

ometric convolutional layer, making it signiﬁcantly

faster and more memory-efﬁcient than MaSIF. Sur-

face ID (Riahi et al., 2023) employs MaSIF for Ab-

Ag interaction predictions.

Additional Ab-Ag-speciﬁc methods have been de-

veloped, such as PECAN (Pittala and Bailey-Kellogg,

2020), which uses a symmetrical graph convolutional

network (GCN) to predict both paratopes and epitopes

within a uniﬁed framework, and EPMP (Del Vec-

chio et al., 2021), which separates the prediction

models for paratopes and epitopes. GEP (geometric

epitope–paratope) prediction (Pegoraro et al., 2023)

proposes geometric representations of molecules to

create accurate predictors for predicting antibody-

antigen binding sites. The study demonstrates the

signiﬁcance of the surface in this type of interaction

and the usefulness of different geometric represen-

tation information for various tasks. Surface-based

models (OGEP) are more efﬁcient in predicting epi-

tope binding, while graph models (IGEP) are better

for paratope prediction, resulting in signiﬁcant perfor-

mance improvements. However, none of these meth-

ods take into account the binding’s ﬂexibility, which

is a crucial factor to consider.

3 MATERIALS AND METHODS

In this section, we present the dataset used for this

study (Subsection 3.1), followed by an introduction

to the ﬁngerprint method (Subsection 3.2) based on

dMaSIF and how we obtained and integrated ﬂexi-

bility within the model (Subsection 3.3). Before ex-

amining the Ab-Ag interaction, we conducted a pre-

liminary comparison of the performance of PPI and

Ab-Ag interactions.

Table 1: Dataset composition.

Dataset Training Validation Test

PPI 4,449 494 959

Ab-Ag 2,729 303 535

3.1 Dataset

For the PPI task, we used the dMaSIF dataset (Sver-

risson et al., 2021). The dataset contains 4,943

protein-protein complexes used for training and val-

idation (10%), with an additional 959 complexes re-

served for testing. In the case of antibody-antigen

interactions, we downloaded a total of 16,269 Ab-

Ag complexes from the SAbDab database (Dunbar

et al., 2014) (April 2024). We then ﬁltered nanobod-

ies, non-deﬁned antigens, haptens, and non-protein

targets. Furthermore, we excluded structures with a

resolution lower than 4

A. To evaluate the similarity of

antibody structures, we utilized the TM-Score (Zhang

and Skolnick, 2004) and excluded Ab-Ag complexes

where the antibody exhibited a TM-Score ¡ 30%. The

dataset was randomly split, resulting in 3,032 Ab-Ag

complexes for training and validation (10%), and 535

complexes for testing. We conducted hyperparameter

tuning and initial conﬁguration study using the vali-

dation set. A summary of the dataset composition is

presented in Table 1.

3.2 Method

Our method is based on dMaSIF (Sverrisson et al.,

2021), an efﬁcient end-to-end geometric analysis ar-

chitecture. The underlying idea is that geometric and

chemical features provide crucial information about

the protein’s surface, especially for PPIs. The method

overview is shown in Figure 2. The model samples

the surface points and normals of the protein and

proceeds to compute mean and Gaussian curvatures

at multiple scales (Figure 2b and c). Chemical fea-

tures are derived based on atom types and their in-

verse distances to surface points and are processed

through a multi-layer perceptron (MLP) (Figure 2d).

These chemical and curvature features form a 16-

dimensional feature vector (Figure 2e). An MLP is

then utilized to predict orientation scores for each sur-

face point, which are employed to align local coor-

dinates (Figure 2f). Further, trainable convolutions

and MLPs reﬁne the feature vectors (Figure 2g), and

interaction prediction is executed by calculating dot

products between the feature vectors of two proteins

to generate interaction scores (Figure 2h). In the fol-

lowing subsections, we describe how we have added

the concept of ﬂexibility to this process. In Figure 3,

there is a summary of the changes made to the original

model to include ﬂexibility and interactive ﬂexibility.

Improving Antibody-Antigen Interaction Prediction Through Flexibility with ESMFold

605

Figure 2: Overview of the dMaSIF method. The red squares represent areas where ﬂexibility was added.

Figure 3: A) This diagram illustrates how ﬂexibility can be represented on the surface of the protein. For each point on the

surface, we computed the 16 nearest neighbors of the corresponding atom in the structure and assigned a ﬂexibility score to

each of the N points, calculated as the mean value of the ﬂexibility scores of the 16 neighbors. B) Architecture of iterative

ﬂexibility. In comparison to the original dMaSIF model, we incorporated the right block of ﬂexibility as an additional feature

in each MLP block, both before and after the quasi-geodesic convolution. The gray box represents one layer of the network,

which can be repeated to create multiple layers prior to generating the output embeddings of the model.

3.2.1 Data Representation

Each protein is represented by a 3D point cloud that

captures every atom in the protein. Following the

dMaSIF representation, each atom is characterized by

10 geometric features (5+5 mean and Gaussian cur-

vatures) and 6 chemical features (one-hot encoding of

the six most signiﬁcant atoms: C, H, O, N, S, Se).

Additionally, we incorporated the pLDDT score from

ESMFold to indicate residue ﬂexibility. The pLDDT

score ranges from 0 to 100, with higher scores indi-

cating greater certainty in the model’s predictions re-

garding the atom’s folding, while lower scores sug-

gest increased uncertainty in the ﬁnal folding, as il-

lustrated in Figure 4A. Studies have demonstrated

that this score correlates with protein ﬂexibility (Guo

et al., 2024; Rudden et al., 2022; Ma et al., 2023):

higher scores correspond to lower ﬂexibility and vice

versa. The original dMaSIF representation, without

ﬂexibility, had 16 features, whereas our method in-

cludes 17 features.

3.3 Flexibility Score with ESMFold

ESMFold (Lin et al., 2023) uses ESM2, which offers

a comprehensive embedded representation of protein

sequences (Joubbi et al., 2024). At the end of the fold-

ing process, this method generates the pLDDT score

mentioned above. To obtain this score, we folded the

corresponding sequences and generated a PDB ﬁle.

In the resulting PDB ﬁle, the pLDDT score is saved

as the b-factor. One issue we encountered was that

dMaSIF uses protonated structures, whereas the ﬁnal

PDB ﬁles generated by ESMFold do not include hy-

drogen scores. To address this, we created a ﬂexibility

score for each residue instead of individual atoms. In

the end, each atom has a ﬂexibility score correspond-

ing to the residue ﬂexibility, as shown in Figure 4B.

3.3.1 3D Point Cloud Association with the

Flexibility Score

dMaSIF samples some point on the surface and com-

putes the Gaussian curvatures, then the chemical fea-

tures are computed based on atom types and their

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606

Figure 4: A) Example of a prediction using ESMFold. Given an input sequence, ESMFold predicts the three-dimensional

structure, with the pLDDT score reﬂecting the model’s conﬁdence for each structural atom. On the left is the original protein

structure, while the right displays the predicted structure alongside the pLDDT score. The protein structure is PDB 1L8W. B)

Assignment of features for each protein structure. Each atom possesses geometric and chemical features, while ﬂexibility is

uniform across all atoms within a single residue.

inverse distances to surface points. These features

are then processed through a multi-layer perceptron

(MLP) with six hidden units, ReLU activation, and

batch normalization. In our model, to report the ﬂexi-

bility on the protein’s surface, as shown in Figure 3A,

we only performed a 16 nearest-neighbor search since

ESMFold has already pre-processed this feature. We

took the average ﬂexibility score of these 16 neigh-

bors for each point. Finally, these features are con-

catenated into a vector of 17 elements.

3.3.2 dMaSIF Network Modiﬁcations

The network is based on trainable convolutions,

MLPs, and batch normalization for the feature vec-

tors. We evaluated two options for incorporating the

ﬂexibility feature: using it directly or employing iter-

ative ﬂexibility layers. We chose iterative layers be-

cause ﬂexibility accounts for only 1/17 of the features,

and interactively adding it helps amplify its signiﬁ-

cance. This adjustment resulted in a feature vector

with 18 elements, as shown in Figure 3B. For inter-

action prediction, dot products are computed between

the feature vectors of both proteins to generate inter-

action scores.

Figure 5: Ablation study for the different combinations of

features. ”geom” denotes geometrical features, ”chem” rep-

resents chemical features, and ”ﬂex” indicates ﬂexibility.

The different models are the following: ”PPI ﬂex” = model

trained on PPI data using ﬂexibility; ”PPI iter” = model

trained on PPI data using iterative ﬂexibility; ”PPI ﬂex

(Ab)” = inference on Ab-Ag complexes using the model

trained on PPI + ﬂexibility, ”PPI iter (Ab)” = inference on

Ab-Ag complexes using the model trained on PPI + iterative

ﬂexibility; ”Ab-Ag ﬁne ﬂex” = model ﬁne-tuned on Ab-Ag

complex + ﬂexibility; ”Ab-Ag ﬁne iter” = model ﬁne-tuned

on Ab-Ag complex + iterative ﬂexibility; ”Ab-Ag ﬂex” =

model trained from scratch on Ab-Ag complexes + ﬂexibil-

ity; ”Ab-Ag iter” = model trained from scratch on Ab-Ag

complexes + iterative ﬂexibility.

Improving Antibody-Antigen Interaction Prediction Through Flexibility with ESMFold

607

Table 2: Results are presented in terms of ROC-AUC for the 5-fold cross-validation on the test set. The ﬁrst three columns

represent the model trained on PPI (PPI), the inference on Ab-Ag (Ab-Ag inference), and the ﬁne-tuning on Ab-Ag (Ab-Ag

ﬁne-tuning). The ﬁnal column indicates the model trained from scratch using Ab-Ag structures (Ab-Ag). The ’Original’ row

represents the model without ﬂexibility, the ’Flexibility’ row denotes the model with the ﬂexibility feature, and the ’Iterative

Flexibility’ row presents the results for the iterative model with ﬂexibility. The best result from each experiment is highlighted

in bold.

Model PPI

Ab-Ag

inference

Ab-Ag

ﬁne-tuning

Ab-Ag

Original 0.835±0.002 0.832±0.004 0.898±0.004 0.881±0.004

Flexibility 0.783±0.003 0.765±0.017 0.863±0.006 0.895±0.002

Iterative

ﬂexibility

0.778±0.008 0.765±0.011 0.866±0.002 0.910±0.002

4 RESULTS

4.1 Cross-Validation

As an initial approach to the Ab-Ag interaction prob-

lem, we assessed whether the dMaSIF model, both

with and without ﬂexibility, could effectively gener-

alize to the Ab-Ag interaction task. We trained the

dMaSIF model using PPI data, as this dataset has

been successfully utilized in prior applications of the

model. As indicated in Table 2, the inclusion of ﬂex-

ibility in the PPI data did not improve predictions

both for PPI and Ab-Ag interaction tasks. In a sub-

sequent attempt, we ﬁne-tuned the PPI-trained model

using Ab-Ag data, which resulted in improved per-

formance; however, the model with ﬂexibility did not

outperform the one without it. Ultimately, we trained

the model from scratch using Ab-Ag data, and in

this scenario, the incorporation of ﬂexibility signiﬁ-

cantly enhanced performance. These results demon-

strate that Ab-Ag interactions represent a speciﬁc cat-

egory of PPI and highlight the necessity for a dedi-

cated model to better characterize them, as well as the

beneﬁts of including ﬂexibility to enhance results. Ta-

ble 2 shows the results of the 5-fold cross-validation.

4.2 Comparison with OGEP

We compared our model with OGEP, the leading

benchmark method for analyzing antibody-antigen in-

teractions based on surface data. We used the GEP

test set, excluding any Protein Data Bank (PDB) en-

tries that overlapped with our training data to en-

sure a fair comparison. This ﬁltering process re-

sulted in a test set of 29 unique PDB entries used

with Ab-Ag iterative ﬂexibility. Although the com-

parison is primarily indicative due to the limited data

available, our ﬁndings indicate that our model, which

was trained on Ab-Ag from scratch using iterative

ﬂexibility, demonstrates signiﬁcantly superior perfor-

mance compared to OGEP (PINet) for antigen in-

teractions (OGEP AUC-ROC: 0.77±0.03 vs. Ab-

Ag iterative AUC-ROC: 0.97±0.00). Additionally, it

achieves comparable performance for antibody inter-

actions (OGEP AUC-ROC: 0.77 ± 0.02 vs. Ab-Ag

iterative AUC-ROC: 0.75 ± 0.01).

4.3 Impact of the Different Features on

Final Prediction

In this work, we conducted an ablation study focusing

on various model features to evaluate the importance

of ﬂexibility in protein-protein interactions (PPI) and

antibody-antigen (Ab-Ag) interactions. We analyzed

all possible combinations of three primary feature

groups: geometrical, chemical, and ﬂexibility. As il-

lustrated in Figure 5, all methods are inﬂuenced by

both chemical and ﬂexibility features, although their

dependence on individual features varies. The PPI in-

teraction models place a greater emphasis on chemi-

cal attributes. Conversely, the ﬁne-tuning model sug-

gests that ﬂexibility features alone have become in-

creasingly important for predictions, except for the

model utilizing iterative ﬂexibility, where geometri-

cal features assume a more signiﬁcant role. Similar

trends were observed in the Ab-Ag interaction model

trained from scratch, highlighting that pLDDT pro-

vides robust predictive features. This highlights the

critical role of the ﬂexibility score in Ab-Ag interac-

tions.

5 CONCLUSIONS

Antibody-antigen interactions are critical molecu-

lar events forming the basis for immune recogni-

tion and neutralization of pathogens or foreign sub-

stance. While different computational approaches has

been developed to model antibody-antigen interac-

tion, most overlook protein ﬂexibility. By incorporat-

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608

ing pLDDT scores from ESMFold as a proxy for ﬂex-

ibility, we demonstrated a 3% improvement in predic-

tion accuracy, achieving an AUC-ROC of 91%. No-

tably, models that explicitly prioritized ﬂexibility out-

performed those that considered ﬂexibility to a lesser

extent, highlighting its signiﬁcance in enhancing pre-

dictive capabilities. While this represents an initial ef-

fort to integrate ﬂexibility into antibody-antigen mod-

eling, future approaches could utilize experimentally

derived conﬁgurations of antibody-antigen complexes

or energy-based models to simulate this dynamic be-

havior more effectively.

A key limitation of the current method is its re-

liance on pre-processed pLDDT scores, which in-

troduces computational overhead. To address this,

we propose incorporating structural distillation tech-

niques to embed ﬂexibility-related insights directly

into sequence-based models, thereby eliminating the

need for structural preprocessing. This adaptation

would streamline workﬂow and enhance accessibility

for experimental laboratories by enabling rapid high-

throughput screening of antibody libraries.

In practical terms, this methodology holds

promise for applications such as epitope mapping

and evaluating binding interactions. By identifying

promising antibody candidates earlier in the process,

researchers can concentrate experimental resources

on the most viable options, accelerating the develop-

ment of effective antibody therapies.

DATA AVAILABILITY

The data and code can be accessed at the following

link: https://github.com/dasch-lab/ﬁngerprint.

ACKNOWLEDGEMENTS

This work is partially supported by PNRR

ECS00000017 Tuscany Health Ecosystem - Spoke

6 ”Precision medicine & personalized healthcare”,

funded by the European Commission under the

NextGeneration EU program. We thank the Univer-

sity of Pisa Data Center for providing the necessary

hardware resources for this project. We thank Pietro

o and St

ephane M. Gagn

e for their valuable

feedback.

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APPENDIX

Environment Settings

The hardware and software resources used are pre-

sented in Table 3.

Table 3: Development environments and requirements.

System Ubuntu 20.04.5 LTS

CPU AMD EPYC 7413 24-Core Pro-

cessor

RAM 16×4GB; 2.67MT/s

GPU NVIDIA A100-SXM-80GB

CUDA

version

11.5

Programming

language

Python 3.8.18

Deep learning

framework

Pytorch (Paszke et al., 2019)

(Torch 1.12.1, torchvision

0.13.1, torchaudio 0.12.1)

Model Training and Hyperparameters

For dMaSIF pre-training on protein-protein interac-

tions (PPI) and ﬁne-tuning on antibody-antigen (Ab-

Ag) interactions, we used a 9.0 radius, 8 embedding

dimensions, and one layer. For Ab-Ag models trained

from scratch, the non-ﬂexibility version used the same

parameters as dMaSIF, while the ﬂexibility-enhanced

models used a 10.0 radius, 16 embedding dimensions,

and either 3 layers (non-iterative) or 5 layers (itera-

tive). All models were trained with a batch size of 8

for 50 epochs, utilizing early stopping, binary cross-

entropy loss, and AMSGrad with a learning rate of

3e-4.

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